Question

You ingest 200 mg of medicine and your body removes 15% of it per hour. How long until there is only 40 mg left?

Answer 1

The time after which only 40 mg of medicine left inside body is 9.8 hours

Explanation:

Given as :

The initial quantity of medicine ingest in body = i=200 mg

The final quantity of medicine in body = f= 40 mg

The rate at which body remove medicine = r = 15%

Let The time taken to remove = t hours

According to question

The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body ×
`(1-(\textrm rate)/(100))^(\textrm time)`

I.e f = i ×
`(1-(\textrm r)/(100))^(\textrm t)`

Or, 40 mg = 200 mg ×
`(1-(\textrm 15)/(100))^(\textrm t)`

Or,
`(40)/(200)` =
`(1-(\textrm 15)/(100))^(\textrm t)`

Or , 0.2 =
`((100 - 15)/(100))^(t)`

Or,
`((85)/(100))^(t)` = 0.2

Taking Log both side

So,
`Log_(10)`
`((85)/(100))^(t)` =
`Log_(10)`0.2

Or, t ×
`Log_(10)`0.85 =
`Log_(10)`0.2

Or, t (-0.07) = - 0.69

∴ t =
`(.69)/(.07)`

I.e t = 9.8 hours

So, The time after which only 40 mg left inside body = t = 9.8 hours

Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer